Convolutional Codes

Today, we are going to talk about:
Another class of linear codes, known as
Convolutional codes.
Structures of the encoder and different
ways for representing it.: state diagram and
trellis representation of the code.
What is a Maximum likelihood decoder?
How the decoding is performed for
Convolutional codes (the Viterbi
algorithm) ?

In block coding, the encoder accepts kbit
message block and generates n-bit
codeword⇒Block-by-block basis
Encoder must buffer an entire message
2
block before generating the codeword
When the message bits come in serially
rather than in large blocks, using buffer
is undesirable
Convolutional coding

The two fundamental building blocks of a digital communication system are modulation and channel coding. They enable reliable communication by providing signaling schemes and receiver structures that utilize the available spectrum and power efficiently.

The properties of Convolutional codes.
We introduced interleaving as a means
to combat bursty errors by making the
channel seem uncorrelated.
We also studied “Concatenated codes”
that simply consist of inner and outer
codes. They can provide the required
performance at a lower complexity.

Low-density parity-check (LDPC) codes are forward error-correction codes,
first proposed in the 1962 PhD thesis of Gallager at MIT. At the time, their
incredible potential remained undiscovered due to the computational demands
of simulation in an era when vacumm tubes were only just being replaced by
the first transistors. They remained largely neglected for over 35 years. In the
mean time the field of forward error correction was dominated by highly structured
algebraic block and convolutional codes.

Another class of linear codes, known as
Convolutional codes.
We study the structure of the encoder.
We study different ways for representing
the encoder.Convolutional codes offer an approach to error control
coding substantially different from that of block codes.
A convolutional encoder:
encodes the entire data stream, into a single codeword.
does not need to segment the data stream into blocks of fixed
size (Convolutional codes are often forced to block structure by periodic
truncation).
is a machine with memory.

Another class of linear codes, known as
Convolutional codes.
We studied the structure of the encoder
and different ways for representing it.What are the state diagram and trellis
representation of the code?
How the decoding is performed for
Convolutional codes?
What is a Maximum likelihood decoder?
What are the soft decisions and hard
decisions?
How does the Viterbi algorithm work?

How decoding is performed for
Convolutional codes?
What is a Maximum likelihood decoder?
What are soft decisions and hard
decisions?
How does the Viterbi algorithm work?The demodulator makes a firm or hard decision
whether one or zero was transmitted and provides
no other information for the decoder such as how
reliable the decision is.